{"title":"Improved Breitung and Roling estimator for mixed-frequency models with application to forecasting inflation rates","authors":"","doi":"10.1007/s00362-023-01520-2","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth <span> <span>\\({SLS}_{1}\\)</span> </span>) for estimating mixed-frequency models. This <span> <span>\\({SLS}_{1}\\)</span> </span> approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in <span> <span>\\({SLS}_{1}\\)</span> </span> solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (<span> <span>\\({SLS}_{2}\\)</span> </span>). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of <span> <span>\\({SLS}_{2},\\)</span> </span> compared to that of <span> <span>\\({SLS}_{1}\\)</span> </span>. Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed <span> <span>\\({SLS}_{2}\\)</span> </span> estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R<sup>2</sup>, which in turn leads to better forecasts.</p>","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"15 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Papers","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00362-023-01520-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth \({SLS}_{1}\)) for estimating mixed-frequency models. This \({SLS}_{1}\) approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in \({SLS}_{1}\) solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (\({SLS}_{2}\)). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of \({SLS}_{2},\) compared to that of \({SLS}_{1}\). Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed \({SLS}_{2}\) estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts.
期刊介绍：
The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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